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Lunar Crater Identification via Deep Learning

Ari Silburt, Mohamad Ali-Dib, Chenchong Zhu, Alan Jackson, Diana Valencia, Yevgeni Kissin, Daniel Tamayo, Kristen Menou

arXiv:1803.02192v3astro-ph.EP

TL;DR

Crater counting is important for studying Solar System history, yet manual detection is limited in scale, efficiency, completeness, and consistency. This paper trains a CNN on Lunar DEM images and transfers it to Mercury, recovering most test-set craters while substantially expanding detections. The results support deep learning as a tool for automated crater extraction across Solar System bodies.

  • Problem

    Manual crater detection limits the scope, efficiency, and accuracy of retrieving craters needed to constrain Solar System history.

  • Method

    The paper trains a CNN to identify crater positions and sizes from Lunar DEM images and transfer-learns it to Mercury.

  • Results

    92% of craters were recovered from the human-generated test set, while the total number of crater detections nearly doubled.

  • Takeaways & Limitations

    The results suggest deep learning can rapidly and automatically extract craters on various Solar System bodies.

  • Takeaways & Limitations

    The CNN tends to miss larger craters, and the estimated false positive rate of new craters is likely too high for the catalog.

Abstract

from arXiv · show

Crater counting on the Moon and other bodies is crucial to constrain the dynamical history of the Solar System. This has traditionally been done by visual inspection of images, thus limiting the scope, efficiency, and/or accuracy of retrieval. In this paper we demonstrate the viability of using convolutional neural networks (CNNs) to determine the positions and sizes of craters from Lunar digital elevation maps (DEMs). We recover 92% of craters from the human-generated test set and almost double the total number of crater detections. Of these new craters, 15% are smaller in diameter than the minimum crater size in the ground-truth dataset. Our median fractional longitude, latitude and radius errors are 11% or less, representing good agreement with the human-generated datasets. From a manual inspection of 361 new craters we estimate the false positive rate of new craters to be 11%. Moreover, our Moon-trained CNN performs well when tested on DEM images of Mercury, detecting a large fraction of craters in each map. Our results suggest that deep learning will be a useful tool for rapidly and automatically extracting craters on various Solar System bodies. We make our code and data publicly available at https://github.com/silburt/DeepMoon.git and https://doi.org/10.5281/zenodo.1133969 .

1. Introduction

Crater catalogs support Solar System history and impactor studies, but manual detection is inefficient, incomplete, and inconsistent across regions and observers. The paper therefore investigates CNN-based crater identification on Lunar DEMs and transfer to Mercury.

  • Crater records and chronology constrain inferences about the Solar System’s dynamical history and formation theories.
  • Crater size distributions probe the dynamics and size distribution of the impactor population.
  • Manual visual inspection is impractical for the Moon’s vast populations of kilometre- and sub-kilometre-sized craters.
  • Human-generated databases trade spatial coverage against crater-size coverage or geographic scope.
  • 40% disagreements can occur among expert crater counts.
  • The study trains a CNN on Lunar DEM images and transfer-learns it for crater identification on Mercury.

2. Methods

The method generates projected, normalized Lunar DEM crops with binary crater-ring targets, trains on catalog-derived image-target pairs, and evaluates a CNN against incomplete human catalogs. Binary ring targets were selected because they were best reproduced, especially with overlapping craters.

  • Data preparation: Input images are randomly cropped, downsampled to 256 × 256 pixels, orthographically projected, and contrast-rescaled.
  • Data preparation: Ground-truth targets encode catalog craters as one-pixel-thick binary rings with catalog-derived centers and radii.
  • Target design: Binary ring targets were reproduced best by the CNN, particularly for images containing many overlapping craters.
  • Data preparation: The target catalogs merge Povilaitis et al. (2017) for 5 −20 km craters with Head et al. (2010) for > 20 km craters.
  • Data preparation: Each of the training, validation, and test datasets contains 30000 DEM images, with a median of 21 craters per image.

2.2. Convolutional Neural Networks (CNNs)

CNNs map images through locally connected, weight-sharing convolutional layers that preserve spatial structure while learning features. In this paper, the network maps DEM images to pixel-wise output targets for segmentation.

  • A neural network stacks layers whose outputs feed subsequent layers, and training tunes weights to approximate ground-truth targets.
  • The paper uses CNN image-to-image mapping, where pixel-intensity inputs are transformed into another two-dimensional array.
  • CNN neurons connect locally and share convolutional weights, embedding image spatial continuity into the architecture.
  • Weight sharing reduces stored and trainable parameters while allowing useful filters to be reused across image regions.
  • Convolutional layers produce feature maps, pooling downsamples spatial dimensions, and merge layers combine compatible feature maps.
  • UNET uses skip connections to merge deep and shallow layers, combining spatial and semantic information for later convolutions.

2.3. CNN Architecture

The model is a custom UNET-like encoder–decoder that processes Lunar DEM images and outputs pixel-wise crater-ring scores. Contracting and expansive paths are linked by multi-level skip connections.

  • The architecture has contracting and expansive paths joined through multi-level skip connections.
  • Lunar DEM images enter the contracting path, and predictions emerge from a final layer after the expansive path.
  • Contracting blocks use two convolutions followed by 2 × 2 max pooling, whereas expansive blocks upsample, concatenate, apply dropout, and convolve twice.
  • The final 1 × 1 convolution uses sigmoid activation and one filter to output pixel-wise class scores.
  • The CNN differs from original UNET in filter counts selected for GPU memory and dropout in the expansive path.

2.4. Crater Extraction

The CNN produces target images containing activated pixels associated with crater rims, but a separate pipeline extracts crater positions and sizes. Template matching scans candidate rings across positions and radii, then thresholds, classifies, and deduplicates detections.

  • A 256 × 256 DEM image passed through the CNN produces a 256 × 256 output target.
  • The CNN does not explicitly extract crater position and size, so a custom pipeline performs this task separately.
  • Template matching slides generated rings through each target and calculates match probabilities at each (x, y, r) coordinate.
  • Pixel intensities above threshold B are set to 1, while lower intensities are set to 0 before template matching.
  • Rings with match probability greater than Pm are classified as craters, and duplicate detections retain only the highest-probability crater.
  • B = 0.1, Pm = 0.5, Dx,y = 1.8 and Dr = 1.0 yield an optimal F1 score of 0.74, with rmin = 5 and rmax = 40.

2.5. Post-Processing

Post-processing aggregates detections across overlapping DEM targets, converts pixel coordinates into geographic and kilometer coordinates, and filters duplicates. Validation selects duplicate-filtering hyperparameters using F1 score.

  • 120 ± 30 different DEM images contain each crater on average, increasing detection likelihood but creating many duplicates across targets.
  • The pipeline aggregates detections across targets, converts pixel coordinates to degrees and kilometers, and removes duplicates.
  • Predicted crater coordinates (x, y, r) are converted into longitude, latitude, and kilometer coordinates using known DEM properties.
  • Duplicate craters are identified using positional and radius criteria controlled by hyperparameters tuned on validation data.
  • DL,L = 2.6 and DR = 1.8 yield an optimal F1 score of 0.67.

2.6. Accuracy Metrics

The paper evaluates crater extraction with precision, recall, F1 score, coordinate errors, and new-crater percentage. These metrics are interpreted cautiously because the ground-truth datasets are incomplete.

  • Precision and recall measure accuracy using true positives, false positives, and false negatives.
  • F1 score is a single-parameter metric that balances precision and recall.
  • Incomplete ground truth causes genuine new craters to be interpreted as false positives, penalizing the loss functions.
  • Fractional errors are calculated separately for predicted crater longitude, latitude, and radius relative to ground-truth values.
  • New-crater percentage counts CNN detections without corresponding ground-truth matches, which may represent genuine new craters or false positives.

2.7. Training

Training uses separate datasets, validation-based hyperparameter selection, and augmentation to limit overfitting. A final test set evaluates generalization to unseen examples.

  • Hyperparameters include convolutional filter size, network depth, learning rate, dropout, and weight regularization.
  • Comparable test, training, and validation accuracy indicates minimal overfitting and likely generalization to new examples.
  • Training, validation, and test examples are split into three separate datasets.
  • Random flips, rotations, and shifts augment the effective dataset and minimize features related to image orientation.
  • The model is selected by training 60 models with randomly chosen hyperparameters and choosing the best validation binary cross-entropy score.

2.8. Errors

The pipeline’s crater-coordinate errors arise from pixel quantization, projection distortion, and approximations in the longitude–latitude mapping. These effects are generally modest but impose a trade-off: minimum-radius filtering reduces errors while excluding the smallest craters.

  • Quantization: Pixel-level detection introduces quantization error, which can affect extracted crater coordinates.The pipeline detects craters only in pixel increments, then converts pixel positions into geographic coordinates.
  • Quantization: 0.1° or ∼3 km is the estimated quantization error for the largest DEM images.This estimate assumes Coffset = 1, a constant of order unity representing typical sub-pixel offsets.
  • Projection distortion: Orthographic projection increasingly distorts objects farther from the central longitude and latitude, altering crater size and shape.For the largest DEM images, the distortion factor is approximately 1.02, producing deviations of at most 2% of a crater’s radius.
  • Error mitigation: A minimum search radius of rmin = 5 prevents quantization and projection errors from becoming a significant fraction of crater radius.The trade-off is reduced sensitivity to the smallest craters in each DEM image, yielding fewer new detections.

3. Results

The CNN pipeline recovers most human-labeled lunar craters while adding many detections, including craters below the ground-truth size limit, with coordinate errors generally at or below 11%. It also produces crater size distributions broadly consistent with human classifications and generalizes to Mercury DEMs, although performance is constrained for large craters and transfer learning was not analyzed exhaustively.

  • 3.1. Crater Identification on the Moon: 92% post-processed test recall recovers almost all craters from the human-generated test set.Post-CNN recall is 57% ± 20%, while aggregation across multiple images and scales raises the final post-processed recall.
  • 3.1. Crater Identification on the Moon: 42% of post-processed test craters are new, almost doubling the catalog, and 15% of these have diameters under 5 km.The estimated false positive rate for these new craters is 11% ± 7%, based on four scientists classifying 361 detections.
  • 3.1. Crater Identification on the Moon: Median post-processed and post-CNN fractional errors in longitude, latitude, and radius are 11% or less.These errors represent overall agreement with the ground-truth dataset despite identified coordinate-error sources.
  • 3.2. Lunar Crater Size Distribution: Between roughly 5 and 20 km, the CNN-derived CSFD is systematically higher yet essentially parallel to the human-derived CSFD.The newly identified craters therefore follow the same size distribution as human-identified craters in this range.
  • 3.2. Lunar Crater Size Distribution: The CNN prediction rolls over below around 5 km but still finds many craters smaller than 5 km.At larger diameters, the CNN and human CSFDs diverge, partly because the CNN struggles with crater radii above approximately 15 pixels.
  • 3.3. Transfer Learning on Mercury: The Moon-trained CNN detects both Mercury crater types despite visible differences between the bodies’ craters.The Mercury results indicate successful generalization, while a thorough transfer-learning analysis is left for future work.

4. Discussion

The CNN learned crater-relevant features and recovered many human-labeled craters while substantially expanding detections, including successful transfer from the Moon to Mercury. Performance is constrained by incomplete ground truth, reduced sensitivity to large craters, and post-processing errors that limit high-precision cataloging.

  • Detection performance: 92% of craters were recovered on the test set, while the CNN’s detections included 42% new Lunar craters.The authors describe these results as evidence of robust crater detection despite incomplete training targets.
  • Cross-body transfer: The Moon-trained CNN successfully detected craters on Mercury, supporting generalization beyond the lunar surface.The discussion links this result to learned crater features rather than features specific to a particular lunar region.
  • Learned features: The CNN activated almost exclusively crater rims rather than non-crater features such as mountains and ridges.Predicted boundaries could be non-circular and sometimes matched true rims better than circular rings.
  • Training-data limitations: Incomplete and inconsistent ground truth makes genuine new detections appear as false positives, producing conservative hyperparameter choices and predictions.A uniformly generated human dataset spanning simple and complex craters is identified as necessary for disentangling dataset effects from morphology effects.

5. Conclusions and Future Work

The study demonstrates that CNNs can identify Lunar craters from DEMs, recover many human-identified craters, and detect substantially more candidates. The Moon-trained CNN also transfers to Mercury, while smaller-crater detection and detailed Mercury analysis remain future work.

  • 92% of craters were recovered from the test set, while total crater identifications nearly doubled.
  • The Moon-trained CNN accurately detected craters in substantially different Mercury DEM images, indicating robust crater detection beyond Moon-specific surface features.
  • Consistency and speed are primary advantages over human crater identification, with predictions for tens of thousands of Lunar DEMs generated in minutes.
  • The CNN can assist human experts by generating initial crater suggestions for verification.
  • Although transfer learning from the Moon to Mercury was successful, detailed Mercury analysis was left to future work.
  • The current work detected craters down to roughly 3 km diameter, while arbitrary image magnification may support transfer learning at kilometer and sub-kilometer scales.
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